A status update on the determination of LNf=3 MS by the ALPHA collaboration

The ALPHA collaboration aims to determine as(mZ) with a total error below the percent level. A further step towards this goal can be taken by combining results from the recent simulations of 2+1-flavour QCD by the CLS initiative with a number of tools developed over the years: Renormalized couplings in finite volume schemes, recursive finite size techniques, two-loop renormalized perturbation theory and the (improved) gradient flow on the lattice. We sketch the strategy, which involves both the standard SF coupling in the high energy regime and a gradient flow coupling at low energies. This implies the need for matching both schemes at an intermediate switching scale, Lswi, which we choose roughly in the range 2-4 GeV. In this contribution we present a preliminary result for this matching procedure, and we then focus on our almost final results for the scale evolution of the SF coupling from Lswi towards the perturbative regime, where we extract the Nf = 3 L-parameter, Λ(3) /MS, in units of Lswi. Connecting Lswii and thus the L-parameter to a hadronic scale such as FK requires 2 further ingredients: first, the connection of Lswii to Lmax using a few steps with the step-scaling function of the gradient flow coupling, and, second, the continuum extrapolation of LmaxFK.